Stochastic Modeling of Nonlinear Random Vibrations Using Heavy-tailed Mixture Distribution

Abstract

In this study, we propose a simple probability density function (PDF) model of Gaussian-Laplacian mixture (GLM) type, which provides a concise parameterization of heavy-tailed data. We construct our model as convex combination of Gaussian and Laplacian PDFs to obtain a minimal parameterization of heavy-tailed data. We then conduct least-squares fitting of our model to a heavy-tailed data generated by a random Duffing oscillator and obtain over 94% of residual sum of squares (RSS) fitness. The resulting model is applied to predicting transient moment responses and achieves over 90% of RSS fitness to Monte–Carlo simulation results of the original system.